Quadrature rules with (not too many) derivatives

2011/09/01 by Wiersma, Matthew
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1109.0326

Abstract

Quadrature formulas for ∫_a^b f(x) dx where derivative terms need only be evaluated at a and b in the composite rule are identified. Error bounds are given when f:[a,b]→ℝ satisfies f^(n-1) is absolutely continuous so that f⁽ⁿ⁾∈ L^p([a,b]), and when f^(n-1) is merely continuous.

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